Maseches Menachos, Chapter 9, Mishnah 3. After listing the various measuring vessels that were in the Mikdash, the Mishnah goes on to list the purpose of each one, beginning with the smallest of them.
"Revi'is mahu meshammeshes":
What was the function of the smallest measure - a revi'is of a log, a quantity of about 125 cc (roughly four ounces)? The Mishnah says that it served two purposes:
A revi'is of water for the metzora.
A revi'is of oil for the nazir.
The metzora, as part of his purification process, brings two birds and living water (spring water) in an earthenware vessel. One of the birds is slaughtered, its blood is placed into the vessel of living water, and the second bird together with the other components is dipped into the mixture of water and blood. How much water was in that mixture? The Tanna of our Mishnah, Rabbi Yishmael (who is not mentioned here by name), holds that the blood must be recognizable within the water, and therefore the amount of water is small - only a revi'is of a log.
It is worth noting that the Mishnah in Nega'im (Chapter 14, Mishnah 1) states that the measure is half a log of water. The Gemara explains that these are two opinions: there it is the view of a Sage, and although the halachah follows him, our Mishnah was taught according to the opinion of Rabbi Yishmael, according to whom a revi'is of a log suffices.
It should also be emphasized that this is not really a sacrificial process: the purification of the metzora was performed in the Beis HaMikdash, just outside the Azarah, and because it was done there, the measuring vessels were readily at hand. The water itself does not acquire inherent sanctity and is not consecrated; the measuring vessel is used purely for the sake of measuring.
The second use is the revi'is of a log of olive oil for the nazir. At the conclusion of his days of nezirus, the nazir brings several offerings, one of which is a ram, and along with it twenty loaves. The tradition is that each of the loaves requires a revi'is of a log of oil. Technically, the oil placed in the revi'is measure is not consecrated by it as a k'li shareis; it is only measured in it, since what gives the oil its inherent sanctity is the slaughtering of the ram that the loaves accompany.
Half a log:
The next measure in size is half a log - about 250 cc, the volume of a cup. What was it used for?
Half a log of water for the sotah - as part of the law of the sotah, the woman suspected of infidelity, water is taken from the Kiyor, a bit of earth from the ground of the Beis HaMikdash is mixed into it, the Name of Hashem from the verses is erased into it, and the woman drinks it. The measure of the water is half a log. Here too this is not an offering, and the water does not acquire inherent sanctity, but it is a process performed in the Mikdash, and therefore this measure had to be ready at hand.
Half a log of oil for the todah - as we learned earlier in the maseches, the todah offering comes with forty loaves of bread: ten of chametz and thirty of matzah. The thirty matzah loaves contain fifteen log of oil in total, and from this we see that each loaf receives half a log of oil.
"U'valog hayah moded l'chol hamenachos":
The log measure was used for all the menachos. This means that every minchah includes one log of olive oil that joins the isaron of fine flour. Of course, there are exceptions, which we have mentioned many times over the course of the tractate:
Menachos with no oil at all: the minchas chotei and the minchas kena'os of the sotah.
Menachos that contain a large amount of oil: the minchas nesachim that accompanies the offerings, and the minchas chavitin of the Kohen Gadol.
The Mishnah continues: "Afilu minchah shel shishim isaron nosen lah shishim log" - even a minchah of sixty isaron is given sixty log. If a person obligated himself to bring not an ordinary minchah of one isaron, but a large minchah of sixty isaron of fine flour, it is given sixty log of oil, and they are measured out one by one with the log vessel. Why did the Mishnah specifically say sixty? In theory a person could obligate himself to bring even a thousand isaron. The answer is that, as we will see further on, the maximum amount that can be placed in a single mixing vessel is sixty isaron, because beyond that there is no proper blilah and the flour will not mix well with the oil.
Rabbi Eliezer ben Yaakov disagrees and says that even a minchah of sixty isaron of fine flour "ein lah ela log" - it has only a log, a single log of oil, so that the minchah turns out far drier. He derives this from the verse: "And one isaron of fine flour mixed with oil... for a minchah, and a log of oil" - from the seemingly superfluous word "for a minchah" he expounds that there is one log of oil regardless of how many esronim the minchah contains. In any case, the halachah follows the first opinion, and this is the fixed ratio: one log of olive oil for every isaron of fine flour.
The larger hin measures:
The hin is twelve log, and its half, its third and its quarter were used for the nesachim that accompany every olah and every shelamim - both for the wine and for the oil of the minchas nesachim:
Six log - for a bull: half a hin. Six log of wine, and six log of oil mixed into three esronim of fine flour - a ratio of two to one.
Four log - for a ram: a third of a hin. A ram is a male sheep of one year, one month and one day. Four log of wine, and four log of oil with two esronim of fine flour - here too a ratio of two to one, twice as oily as the standard.
Three log - for a lamb: a quarter of a hin. Three log of wine, and three log of oil with one isaron of fine flour - a ratio of three to one, the oiliest of all the mixtures.
"Sheloshah u'machatzi lamenorah":
This is a separate point, taught here in connection with the subject of oil and measures: the amount of olive oil used for kindling the Menorah was three and a half log - half a log for each of the lamps. The Menorah, as we recall, has seven branches, and on each of them a cup that was filled with half a log of oil and kindled every night until morning. According to the Rambam the kindling was done twice a day, in the morning and in the evening, but the principle is the same: there must be enough oil to burn through the entire night, as the verse requires.
The Gemara here in Menachos relates that a practical test was conducted to determine how much oil is needed to burn through the whole night, and the conclusion was half a log. But the Gemara asks: nights vary in length, so how can a single measure work for all of them? There are two approaches:
According to the Bavli: they gave a measure sufficient for the longest night of the year. In Jerusalem the winter nights are about fourteen hours and the summer nights about ten hours, so on the shorter nights oil was left over - and this is not a concern, since "there is no poverty in a place of wealth."
According to the Yerushalmi: they adjusted the thickness of the wicks. With a wick of ordinary size, half a log is enough to last from evening until morning in Tishrei and in Nissan; on the long winter nights they used a thinner wick that would burn more slowly, and on the short summer nights a thicker wick that would burn more quickly.
The Rambam makes no mention at all of adjusting the thickness of the wicks, and in his view the measure is always half a log; others, however, including Tosafos, hold that they did indeed adjust the thickness of the wick to the length of the night.